Primality Testing Examples

Number Theory · Axiom Academy

EXAMPLE Primality Testing Examples Master the technique of determining if a number is prime by checking divisibility efficiently Excellent work! You've mastered primality testing. Here's what we learned: Square Root Bound: To test if n is prime, you only need to check divisibility by primes up to √ n . This dramatically reduces the number of checks needed. Check Primes Only: When testing divisibility, we only need to test prime divisors because composite divisors are products of smaller primes. If a composite divides n , then its prime factors already divide n . Systematic Approach: Start with small primes (2, 3, 5, 7, 11, ...) and stop at √ n . If no prime divisor is found, the number is prime. Common Patterns: Check divisibility by 2 first (even numbers), then by 3, 5, 7, etc. Many composite numbers fail quickly at small primes. Verification Process: For each test case, calculate √ n , identify which primes to check, and systematically test each one until you find a divisor or confirm primality. This efficient method will help you quickly determine primality for any number. Practice with different values to build speed and confidence!

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